Statistical Mechanics - Fundamentals

Fundamentals

Fundamentals of Statistical Mechanics at Wikipedia books

Central topics covered in statistical thermodynamics include:

• Microstates and configurations
• Boltzmann distribution law
• Partition function, Configuration integral or configurational partition function
• Thermodynamic equilibrium - thermal, mechanical, and chemical.
• Internal degrees of freedom - rotation, vibration, electronic excitation, etc.
• Heat capacity – Einstein solids, polyatomic gases, etc.
• Nernst heat theorem
• Fluctuations
• Gibbs paradox
• Degeneracy

Lastly, and most importantly, the formal definition of entropy of a thermodynamic system from a statistical perspective is called statistical entropy, and is defined as:

where k_B is Boltzmann's constant 1.38066×10−23 J K−1 and Ω is the number of microstates corresponding to the observed thermodynamic macrostate.

This equation is valid only if each microstate is equally accessible (each microstate has an equal probability of occurring).